Patch antenna array for transmission of Hermite-Gaussian and Laguerre Gaussian beams

ABSTRACT

An antenna array includes a plurality of patch antennas including a plurality of layers. Each of the plurality of layers are separated by a distance and each support a portion of the plurality of patch antennas. A plurality of connectors are each associated with one of the plurality of layers and supply a signal for transmission by the associated layer. A feed network on each of the plurality of layers provides a connection between a connector associated with the layer and the portion of the patch antennas located on the layer. Each layer transmits a signal having a different orthogonal function applied thereto that multiplexes each of the signals having a different orthogonal function applied thereto onto a single transmission beam. A parabolic reflector reflects the single transmission beam from the plurality of layers of the antenna array.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of U.S. patentapplication Ser. No. 15/187,315, filed Jun. 20, 2016, entitled PATCHANTENNA ARRAY FOR TRANSMISSION OF HERMITE-GAUSSIAN AND LAGUERRE GAUSSIANBEAMS (Atty. Dkt. No. NXGN-33142), which claims priority to U.S.Provisional Application No. 62/182,227, entitled PATCH ANTENNAS FORTRANSMISSION OF HERMITE-GAUSSIAN AND LAGUERRE-GAUSSIAN BEAMS, filed onJun. 19, 2015; U.S. Provisional No. 62/233,838, entitled PATCH ANTENNASFOR TRANSMISSION OF HERMITE-GAUSSIAN AND LAGUERRE-GAUSSIAN BEAMS, filedon Sep. 28, 2015; U.S. Provisional Application No. 62/242,056, entitledMETHOD FOR MANUFACTURING A PATCH ANTENNA, filed on Oct. 15, 2015; andU.S. Provisional Application No. 62/311,633, entitled HYBRID PATCHANTENNA WITH PARABOLIC REFLECTOR, filed on Mar. 22, 2016, each of whichis incorporated herein by reference in their entirety.

TECHNICAL FIELD

The present application relates to patch antennas, and more particularlyto patch antennas for the transmission of Hermite-Gaussian andLaguerre-Gaussian Beams.

BACKGROUND

When transmitting Hermite-Gaussian and Laguerre-Gaussian beams, theability to multiplex multiple modes of these type of beams together intoa single signal is needed to provide increased bandwidth. By increasingthe number of Hermite-Gaussian and Laguerre-Gaussian beams that can bemultiplexed together, an increased data throughput can be achieved.Thus, there is a need for antenna and transmission structures thatprovide for multiplexing of Hermite-Gaussian and Laguerre-Gaussianbeams.

SUMMARY

The present invention, as disclosed and described herein, in one aspectthereof comprises a multi-level antenna array including a plurality ofpatch antennas. The antenna further includes a plurality of layers. Eachof the plurality of layers are separated from each other by a distanceand each of the plurality of layers further support a portion of theplurality of patch antennas. A plurality of connectors are eachassociated with one of the plurality of layers and supply a signal fortransmission by the associated layer. A feed network on each of theplurality of layers provides a connection between a connector of theplurality of connectors associated with the layer and the portion of theplurality of patch antennas located on the layer. Each layer of theplurality of layers transmits the signal having a different orthogonalfunction applied thereto that multiplexes each of the signals having adifferent orthogonal function applied thereto onto a single transmissionbeam. A parabolic reflector reflects the single transmission beam fromthe plurality of layers of the multi-level antenna array.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding, reference is now made to thefollowing description taken in conjunction with the accompanyingDrawings in which:

FIG. 1 illustrates a top view of a multilayer patch antenna array;

FIG. 2 illustrates a side view of a multilayer patch antenna array;

FIG. 3 illustrates a first layer of a multilayer patch antenna array;

FIG. 4 illustrates a second layer of a multilayer patch antenna array;

FIG. 5 illustrates a transmitter for use with a multilayer patch antennaarray;

FIG. 6 illustrates a multiplexed OAM signal transmitted from amultilayer patch antenna array;

FIG. 7 illustrates a receiver for use with a multilayer patch antennaarray;

FIG. 8 illustrates a microstrip patch antenna;

FIG. 9 illustrates a coordinate system for an aperture of a microstrippatch antenna;

FIG. 10 illustrates a 3-D model of a single rectangular patch antenna;

FIG. 11 illustrates the radiation pattern of the patch antenna of FIG.10;

FIG. 12a illustrates the radiation pattern of a circular array for anOAM mode order 1=0;

FIG. 12b illustrates the radiation pattern for an OAM mode order 1=0 inthe vicinity of the array axis;

FIG. 12c illustrates the radiation pattern for an OAM mode order 1=1 inthe vicinity of the array axis;

FIG. 12d illustrates the radiation pattern for an OAM mode order 1=2 inthe vicinity of the array axis;

FIG. 13 illustrates a multilayer patch antenna array with a parabolicreflector;

FIG. 14 illustrates various configurations of the patch antenna andparabolic reflector;

FIG. 15 illustrates a hybrid patch and parabolic antenna using a singlereflector;

FIG. 16 illustrates the simulated results of received power as afunction of transmission distance with a single reflection and doublereflection hybrid patch and parabolic antenna;

FIG. 17 illustrates an OAM multiplexed link using hybrid patch andparabolic antenna with spiral phase plate at a receiver;

FIG. 18 illustrates an OAM multiplexed link using hybrid patch andparabolic antenna for the transmitter and the receiver;

FIG. 19 is a flow diagram illustrating the design and layout process ofa patch antenna;

FIG. 20 is a flow diagram illustrating the process for patterning acopper layer on a laminate for a patch antenna; and

FIG. 21 is a flow diagram illustrating a testing process for amanufactured patch antenna.

DETAILED DESCRIPTION

Referring now to the drawings, wherein like reference numbers are usedherein to designate like elements throughout, the various views andembodiments of a patch antenna array for transmission ofHermite-Gaussian and Laguerre-Gaussian beams are illustrated anddescribed, and other possible embodiments are described. The figures arenot necessarily drawn to scale, and in some instances the drawings havebeen exaggerated and/or simplified in places for illustrative purposesonly. One of ordinary skill in the art will appreciate the many possibleapplications and variations based on the following examples of possibleembodiments.

FIG. 1 illustrates a multilayer patch antenna array 102. The multilayerpatch antenna array 102 includes a first antenna layer 104 fortransmitting a first ordered beam, a second antenna layer 106 fortransmitting a second ordered beam and a third layer 108 fortransmitting a third ordered beam. Each of the layers 104, 106 and 108are stacked on a same center. While the present embodiment isillustrated with respect to a multilayer patch antenna array 102including only three layers, it should be realized that either more orless layers may be implemented in a similar fashion as described herein.On the surface of each of the layers 104, 106 and 108 are placed patchantennas 110. Each of the patch antennas are placed such that they arenot obscured by the above layer. The layers 104, 106 and 108 areseparated from each other by layer separator members 112 that providespacing between each of the layers 104, 106 and 108. The configurationof the layers of the patch antenna may be in rectangular, circular orelliptical configurations to generate Hermite-Gaussian,Laguerre-Gaussian or Ince-Gaussian beams.

The patch antennas 110 used within the multilayer patch antenna array102 are made from FR408 (flame retardant 408) laminate that ismanufactured by Isola Global, of Chandler Ariz. and has a relativepermittivity of approximately 3.75. The antenna has an overall height of125 μm. The metal of the antenna is copper having a thickness ofapproximately 12 μm. The patch antenna is designed to have an operatingfrequency of 73 GHz and a free space wavelength of 4.1 mm. Thedimensions of the input 50 Ohm line of the antenna is 280 μm while theinput dimensions of the 100 Ohm line are 66 μm.

Each of the patch antennas 110 are configured to transmit signals at apredetermined phase that is different from the phase of each of theother patch antenna 110 on a same layer. Thus, as further illustrated inFIG. 3, there are four patch antenna elements 110 included on a layer104. Each of the antenna elements 104 have a separate phase associatedthere with as indicated in FIG. 3. These phases include π/2, 2(π/2),3(π/2) and 4(π/2). Similarly, as illustrated in FIG. 4 layer 106includes eight different patch antenna elements 110 including the phasesπ/2, 2(π/2), 3(π/2), 4(π/2), 5(π/2), 6(π/2), 7(π/2) and 8(π/2) asindicated. Finally, referring back to FIG. 1, there are included 12patch antenna elements 110 on layer 108. Each of these patch antennaelements 110 have a phase assigned thereto in the manner indicated inFIG. 1. These phases include π/2, 2(π/2), 3(π/2), 4(π/2), 5(π/2),6(π/2), 7(π/2), 8(π/2), 9(π/2), 10(π/2), 11(π/2) and 12(π/2).

Each of the antenna layers 104, 106 and 108 are connected to a coaxialend-launch connector 116 to feed each layer of the multilayer patchantenna array 102. Each of the connectors 116 are connected to receive aseparate signal that allows the transmission of a separate orderedantenna beam in a manner similar to that illustrated in FIG. 2. Theemitted beams are multiplexed together by the multilayered patch antennaarray 102. The orthogonal wavefronts transmitted from each layer of themultilayered patch antenna array 102 in a spatial manner to increasecapacity as each wavefront will act as an independent Eigen channel. Thesignals are multiplexed onto a single frequency and propagate withoutinterference or crosstalk between the multiplexed signals. While theillustration with respect to FIG. 2 illustrates the transmission of OAMbeams at OAM 1, OAM 2 and OAM 3 ordered levels.

It should be understood that other types of Hermite Gaussian andLaguerre Gaussian beams can be transmitted using the multilayer patchantenna array 102 illustrated. Hermite-Gaussian polynomials andLaguerre-Gaussian polynomials are examples of classical orthogonalpolynomial sequences, which are the Eigenstates of a quantum harmonicoscillator. However, it should be understood that other signals may alsobe used, for example orthogonal polynomials or functions such as Jacobipolynomials, Gegenbauer polynomials, Legendre polynomials and Chebyshevpolynomials. Legendre functions, Bessel functions, prolate spheroidalfunctions and Ince-Gaussian functions may also be used. Q-functions areanother class of functions that can be employed as a basis fororthogonal functions.

The feeding network 118 illustrated on each of the layers 104, 106, 108uses delay lines of differing lengths in order to establish the phase ofeach patch antenna element 110. By configuring the phases as illustratedin FIGS. 1-3 the OAM beams of different orders are generated andmultiplexed together.

Referring now to FIG. 5, there is illustrated a transmitter 502 forgenerating a multiplexed beam for transmission. As discussed previously,the multilayered patch antenna array 102 includes a connector 116associated with each layer 104, 106, 108 of the multilayer patch antennaarray 102. Each of these connectors 116 are connected with signalgeneration circuitry 504. The signal generation circuitry 504 includes,in one embodiment, a 60 GHz local oscillator 506 for generating a 60 GHzcarrier signal. The signal generation circuit 504 may also work withother frequencies, such as 70/80 GHz. The 60 GHz signal is output fromthe local oscillator 506 to a power divider circuit 508 which separatesthe 60 GHz signal into three separate transmission signals. Each ofthese separated transmission signals are provided to an IQ mixer 510that are each connected to one of the layer input connectors 116. The IQmixer circuits 510 are connected to an associated additive whitegaussian noise circuit 512 for inserting a noise element into thegenerated transmission signal. The AWG circuit 512 may also generateSuperQAM signals for insertion in to the transmission signals. The IQmixer 510 generates signals in a manner such as that described in U.S.patent application Ser. No. 14/323,082, filed on Jul. 3, 2014, now U.S.Pat. No. 9,331,875, issued on May 3, 2016, entitled SYSTEM AND METHODFOR COMMUNICATION USING ORBITAL ANGULAR MOMENTUM WITH MULTIPLE LAYEROVERLAY MODULATION, which is incorporated herein by reference in itsentirety.

Using the transmitter 502 illustrated in FIG. 5. A multiplexed beam(Hermite Gaussian, Laguerre Gaussian, etc.) can be generated asillustrated in FIG. 6. As illustrated, the multilayered patch antennaarray 102 will generate a multiplexed beam 602 for transmission. In thepresent example, there is illustrated a multiplex OAM beam that hastwists for various order OAM signals in a manner similar to thatdisclosed in U.S. patent application Ser. No. 14/323,082. An associatedreceiver detector would detect the various OAM rings 604 as illustratedeach of the rings associated with a separate OAM processed signal.

When signals are transmitted in free space (vacuum), the signals aretransmitted as plane waves. They may be represented as described hereinbelow. Free space comprises a nonconducting medium (σ=0) and thusJ=σE=0.

From experimental results Ampere's law and Faraday's law are representedas:

$\begin{matrix}{\overset{\rightarrow}{B} = {\mu\;\overset{\rightarrow}{H}}} & {{\nabla{xH}} = {\frac{\partial D}{\partial t} + J}} & {{{Ampere}’}s} \\\; & {\overset{\rightarrow}{D} = {\in \overset{\rightarrow}{E}}} & \; \\{\overset{\rightarrow}{J} = {\sigma\;\overset{\rightarrow}{E}}} & {{\nabla{xE}} = \frac{- {\partial B}}{\partial t}} & {{{Faraday}’}s}\end{matrix}$If there is propagation in the z direction and therefore E and H are inthe xy plane.

Without the loss of any generality E may be oriented in the x-directionand H may be oriented in the y-direction thus providing propagation inthe z-direction. From Ampere's-Maxwell equation, the following equationsare provided:

${\nabla{xH}} = \frac{\partial D}{\partial t}$${\nabla{xH}} = {\begin{matrix}\hat{x} & \hat{y} & \hat{z} \\\frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\H_{x} & H_{y} & H_{z}\end{matrix}}$${{\left( {\frac{\partial{Hz}}{\partial y} - \frac{\partial{Hy}}{\partial z}} \right)\hat{x}} + {\left( {\frac{\partial{Hz}}{\partial z} - \frac{\partial{Hz}}{\partial x}} \right)\hat{y}} + {\left( {\frac{\partial{Hy}}{\partial x} - \frac{\partial{Hx}}{\partial y}} \right)\hat{z}}} = {\frac{\partial}{\partial t} \in E}$

Next, the vectorial wave equations may be represented as:

${\nabla{xH}} = {\frac{\partial D}{\partial t} + J}$${\nabla{xH}} = {\in \frac{\partial E}{\partial t}}$${\nabla{xE}} = \frac{- {\partial B}}{\partial t}$${\nabla{xE}} = {{- \mu}\frac{\partial H}{\partial t}}$ ∇xB = 0 ∇xE = S∇x∇xH = ∇(∇H) − ∇²H = −∇²H ∇x∇xE = ∇(∇E) − ∇²E = −∇²E${\nabla{x\left( {\nabla{xH}} \right)}} = {{\nabla{x\left( {\in \frac{\partial E}{\partial t}} \right)}} = {{\in {\frac{\partial}{\partial t}\left( {\nabla{xE}} \right)}} = {\in {\mu\frac{\partial}{\partial t}\left( {\frac{\partial}{\partial t}H} \right)}}}}$${\nabla^{2}H} = {+ {\in {\mu\frac{\partial^{2}}{\partial t^{2}}H}}}$${{{\nabla^{2}H} -} \in {\mu\frac{\partial^{2}}{\partial t^{2}}H}} = 0$${\nabla{x\left( {\nabla{xE}} \right)}} = {{\nabla{x\left( {{- \mu}\frac{\partial}{\partial t}H} \right)}} = {{{- \mu}\frac{\partial}{\partial t}\left( {\nabla{xH}} \right)} = {{{{- \mu}\frac{\partial}{\partial t}\left( {\in \frac{\partial E}{\partial t}} \right)} + {\nabla^{2}E}} = {{+ \mu} \in {\frac{\partial^{2}}{\partial t^{2}}E}}}}}$${{{\nabla^{2}E} - \mu} \in {\frac{\partial^{2}}{\partial t^{1}}E}} = 0$

Therefore in general:{right arrow over (∇)}² {right arrow over (E)}+{right arrow over (K)} ²{right arrow over (E)}=0E({right arrow over (r)},t){right arrow over (E)}(r,t)={right arrow over (E)}({right arrow over(r)})e ^(−jwt) e ^(jkz) Propagating in z-directionTherefore:

${{\left( {\frac{\partial^{2}}{\partial x^{2}} + \frac{\partial^{2}}{\partial y^{2}} + \frac{\partial^{2}}{\partial z^{2}}} \right){\overset{\rightarrow}{E}\left( \overset{\rightarrow}{r} \right)}e^{- {jwt}}e^{jkz}} + {\frac{w^{2}}{y^{2}}{\overset{\rightarrow}{E}\left( \overset{\rightarrow}{r} \right)}e^{- {jwt}}e^{jkz}}} = 0$In free space

$w = {\frac{1}{\sqrt{\mu \in}} = {\left. \rightarrow c \right. = \frac{1}{\sqrt{\mu \in o}}}}$$k^{2} = \frac{w^{2}}{c^{2}}$Now:

${\frac{\partial}{\partial z}{\overset{\rightarrow}{E}\left( \overset{\rightarrow}{r} \right)}e^{jkz}} = {e^{jkz}\left\lbrack {\frac{\partial{\overset{\rightarrow}{E}\left( \overset{\rightarrow}{r} \right)}}{\partial z} + {{jk}{\overset{\rightarrow}{E}\left( \overset{\rightarrow}{r} \right)}}} \right\rbrack}$$\begin{matrix}{{\frac{\partial}{\partial z}{\overset{\rightarrow}{E}\left( \overset{\rightarrow}{r} \right)}e^{jkz}} = {{e^{jkz}\left\lbrack {\frac{\partial{\overset{\rightarrow}{E}\left( \overset{\rightarrow}{r} \right)}}{\partial z} + {{jk}{\overset{\rightarrow}{E}\left( \overset{\rightarrow}{r} \right)}}} \right\rbrack} + {e^{jkz}\left\lbrack {\frac{\partial^{2}{\overset{\rightarrow}{E}\left( \overset{\rightarrow}{r} \right)}}{\partial z^{2}} + {{jk}\frac{\partial{\overset{\rightarrow}{E}\left( \overset{\rightarrow}{r} \right)}}{\partial z}}} \right\rbrack}}} \\{= {{e^{jkz}\left\lbrack {{{jk}\frac{\partial\overset{\rightarrow}{E}}{\partial z}} - {k^{2}{\overset{\rightarrow}{E}\left( \overset{\rightarrow}{r} \right)}}} \right\rbrack} + {e^{jkz}\left\lbrack {\frac{\partial^{2}\overset{\rightarrow}{E}}{\partial z^{2}} + {{jk}\frac{\partial\overset{\rightarrow}{E}}{\partial z}}} \right\rbrack}}}\end{matrix}$Because

${{2k\frac{\partial E}{\partial z}}} ⪢ {\frac{\partial^{2}{E(r)}}{\partial z^{2}}}$Paraxial assumption

$\frac{{\partial^{2}{\overset{\rightarrow}{E}\left( \overset{\rightarrow}{r} \right)}}e^{jkz}}{\partial z^{2}} = {e^{jkz}\left\lbrack {{2{jk}\frac{\partial^{2}{\overset{\rightarrow}{E}\left( \overset{\rightarrow}{r} \right)}}{\partial z}} - {k^{2}{\overset{\rightarrow}{E}\left( \overset{\rightarrow}{r} \right)}}} \right\rbrack}$Then:

${\left( {\frac{\partial^{2}}{\partial x^{2}} + \frac{\partial^{2}}{\partial y^{2}} + {2{jk}\frac{\partial^{2}}{\partial z}}} \right){E\left( {x,y,z} \right)}} = 0$Which may be represented in cylindrical coordinates as:

${\frac{\partial^{2}}{\partial x^{2}} + \frac{\partial^{2}}{\partial y^{2}}} = {{\frac{1}{q}\frac{\partial}{\partial q}\left( {q\frac{\partial}{\partial q}} \right)} + {\frac{1}{q^{2}}\frac{\partial^{2}}{\partial\Phi^{2}}}}$

This provides a paraxial wave equation in cylindrical coordinates:

${{\frac{1}{q}\frac{\partial}{\partial q}\left( {q\frac{\partial}{\partial q}} \right){E\left( {q,\Phi,z} \right)}} + {\frac{1}{q^{2}}\frac{\partial^{2}}{\partial\Phi^{2}}{E\left( {q,\Phi,z} \right)}} + {2{jk}\frac{\partial E}{\partial z}\left( {q,\Phi,z} \right)}} = o$P(z), q(z)Then:

$E_{0} \sim e^{- {j{\lbrack{p + {\frac{k}{2q}{({x^{2} + y^{2}})}}}\rbrack}}}$

In general E_(o) can rotate on the xy-plane and the wave stillpropagates in the z-direction.

$\frac{\partial q}{\partial z} = 1$$\frac{\partial p}{\partial z} = {- \frac{j}{q}}$

-   -   q˜Curvature of the phase front near the optical axis.        q ₂ =q ₁ +z        where q₂ is the output plane and q₁ is the input plane.∞∞

$\frac{1}{q} = {\frac{1}{R} - {j\frac{\lambda}{\pi\; W^{2}}}}$where

$\frac{1}{R}$is the curvature of the wavefront intersecting the z-axis.

Thus for a complete plane wave R=∞, the equation becomes:

$\frac{1}{q} = {\frac{1}{\left. R\rightarrow\infty \right.} - {j\frac{\lambda}{\pi\; W^{2}}}}$$q_{0} = {\frac{\pi\; W^{2}}{{- j}\;\lambda} = \frac{j\;\pi\; W_{0}^{2}}{\lambda}}$where W_(o) is the beam waist.

$q = {{q_{0} + z} = {\frac{j\;\pi\; W_{0}^{2}}{\lambda} + z}}$${w(z)} = {w_{0}\sqrt{1 + \left( \frac{z}{z_{r}} \right)^{2}}}$${W^{2}(z)} = {W_{0}^{2}\left\lbrack {1 + \left( \frac{\lambda\; z}{\pi\; W_{0}^{2}} \right)^{2}} \right\rbrack}$${R(z)} = {z\left\lbrack {1 + \left( \frac{\pi\; W_{0}^{2}}{\lambda\; z} \right)^{2}} \right\rbrack}$${R(z)} = {z\left\lbrack {1 + \left( \frac{z_{R}}{z} \right)^{2}} \right\rbrack}$${\Phi(z)} = {\tan^{- 1}\left( \frac{z}{z_{R}} \right)}$$\theta = \frac{\lambda}{\pi\; w_{0}}$ z = z_(R)${w(z)} = {\sqrt{2}w_{0}}$

The Rayleigh length is:

$z_{R} = \frac{\pi\; n}{\lambda_{0}}$where n is the index of refraction.

$w_{0}^{2} = \frac{w^{2}}{1 + \left( \frac{\pi\; w^{2}}{\lambda\; R} \right)^{2}}$$z = \frac{R}{1 + \left( \frac{\lambda\; R}{\pi\; w^{2}} \right)^{2}}$

The complex phase shift is represented by:

${j\;{P(z)}} = {{{Ln}\left\lbrack {1 - {j\left( \frac{\lambda\; z}{\pi\; w_{0}^{2}} \right)}} \right\rbrack} = {{{Ln}\sqrt{1 + \left( \frac{\lambda\; z}{\pi\; w_{0}^{2}} \right)^{2}}} - {j\;\tan^{- 1}\frac{\lambda\; z}{\pi\; w_{0}^{2}}}}}$

The real part of P(z) represents a phase shift difference between theGaussian beam and an ideal plane wave. Thus the fundamental mode isprovided:

${E_{0}\left( {x,y,z} \right)} = {{E_{0}\left( {r,z} \right)}\frac{w_{0}}{w}e^{- {j{({{jz} - \phi})}}}e^{- {r^{2}{({\frac{1}{w^{2}} + \frac{j\; k}{2\; R}})}}}}$where:

$\phi = {\tan^{- 1}\frac{\lambda\; z}{\pi\; w_{0}^{2}}}$

Higher order modes may also provide other solutions. The solution ofrectangular equation:

${\left( {\frac{\partial^{2}}{\partial x^{2}} + \frac{\partial^{2}}{\partial y^{2}} + {2\;{jk}\frac{\partial}{\partial z}}} \right){E\left( {x,y,z} \right)}} = 0$Can be determined in rectangular coordinates to be:

${E\left( {x,y,z} \right)} = {\sum\limits_{mn}\;{C_{nm}E_{0}\frac{w_{0}}{w(z)}{H_{m}\left\lbrack \frac{\sqrt{2}x}{w(z)} \right\rbrack}{H_{n}\left\lbrack \frac{\sqrt{2}y}{w(z)} \right\rbrack}e^{\frac{- {({x^{2} + y^{2}})}}{{w{(t)}}^{2}}}e^{{- {j{({m + m + 1})}}}t\;{an}^{- 1}\frac{z}{z_{0}}}e^{j\frac{k{({x^{2} + y^{2}})}}{2{R{(z)}}}}}}$$z_{0} = \frac{{kw}_{0}^{2}}{2}$${w(z)} = {w_{0}\sqrt{1 + \frac{z^{2}}{z_{0}^{2}}}}$ C₆₀ ⇒ TEM_(OD)${R(z)} = {{z + \frac{z_{0}^{2}}{z}} = {{\frac{z_{0}^{2}}{z}\left( {1 + \frac{z^{2}}{z_{0}^{2}}} \right)} = {{\frac{z_{0}^{2}}{{zw}_{0}^{2}}{w^{2}(z)}} = {\frac{{kz}_{0}}{2\; z}{w^{2}(z)}}}}}$

The solution of cylindrical coordinates of equation:

${{\frac{1}{\rho}\frac{\partial}{\partial\rho}\left( {\rho\frac{\partial}{\partial\rho}} \right){E\left( {\rho,\varnothing,z} \right)}} + {\frac{1}{\rho^{2}}\frac{{\partial^{\bigwedge}2}\;{E\left( {\rho,\varnothing,z} \right)}}{{\delta\varnothing}^{2}}} + {2{jk}\frac{\partial{E\left( {\rho,\varnothing,z} \right)}}{\partial z}}} = 0$Can be determined in cylindrical coordinates to be:

${E\left( {\rho,\varnothing,z} \right)} = {\sum\limits_{l\;\rho}\;{C_{l\;\rho}E_{0}\frac{w_{0}}{w(z)}\left( \frac{\sqrt{2}\rho}{w(z)} \right)^{l}{L_{l}^{\rho}\left( \frac{\sqrt{2}\rho}{w(z)} \right)}e^{{- \frac{\rho^{2}}{{w^{2}{(t)}}_{e}}} - {{j{({{2\rho} + l + 1})}}t\;{an}^{- 1}\frac{z}{z_{0}}}}e^{j\; l\;\varnothing}e^{j\frac{k\;\rho^{2}}{2{R{(z)}}}}}}$The equation

$L_{l}^{\rho}\left( \frac{\sqrt{2\rho}}{w(z)} \right)$may also be shown as

${L_{l}^{\rho}\left\lbrack \frac{2\rho^{2}}{w^{2}(t)} \right\rbrack}.$

The lowest mode is the most important mode and in fact this transversemode is identical for both rectangular and cylindrical coordinates.

${\varphi\left( {l,{P;z}} \right)} = {\left( {{2\; P} + l + 1} \right)\tan^{- 1}\frac{z}{z_{0}}}$TEM₀₀^(rect) = TEM₀₀^(Cyl) C₀₀ = 1 H₀ = 1 L₀⁰ = 1 then$\left. {TEM}_{00}\Rightarrow{{E\left( {\rho,z} \right)} \sim {E_{0}\frac{w_{0}}{w(z)}e^{- \frac{\rho^{2}}{w^{2}{(t)}}}e^{{- j}\;\tan^{- 1}\frac{z}{z_{0}}}e^{{jk}\frac{\rho^{2}}{2\;{R{(z)}}}}}} \right.$

Referring now to FIG. 7, there is illustrated a receiver 702 fordemultiplexing signals received from a multiplexed signal generatedusing the transmitter 502 of FIG. 5. The receiver 702 includes amultilayer patch antenna array 102 such as that described herein above.The multilayer patch antenna array 102 receives the incoming multiplexedsignal 704 and each layer 104, 106, 108 of the antenna array 102 willextract a particular order of the received multiplexed signal from eachof the connector outputs 116 of a particular layer. The signals fromeach of the connectors 116 are applied to a mixer circuit 706 thatdemultiplexes the received signal in a manner similar to that discussedwith respect to U.S. patent application Ser. No. 14/323,082 using a 60GHz local oscillator signal from oscillator 708. The demultiplexedsignal may then be read using, for example, a real-time oscilloscope 710or other signal reading device. Each of the three transmitted signals isthus decoded at the receiver 702 that were transmitted in each of theordered OAM signals received from the transmitters 602. In a furtherembodiment, a demultiplexing approach using SPP (spiral phase plate) mayalso be applied to detect OAM channels.

The signals transmitted by the transmitter 502 or the receiver 702 maybe used for the transmission of information between two locations in avariety of matters. These include there use in both front haulcommunications and back haul communications within a telecommunicationsor data network.

Referring now more particularly to FIG. 8, there is illustrated a patchantenna element 110. Multiple ones of these patch antenna elements 110are located upon the multilayer patch antenna array 102 as discussedhereinabove. The antenna element 110 includes a patch 802 having alength L and a width W. The patch 802 is fed from an input transmissionline 804 that is connected with the feed network 104 (FIG. 1) and isresting upon a substrate 806 having a height h. The microstrip patchantenna includes a first radiating slot 808 along a first edge of thepatch 802 and a second radiating slot 810 along a second edge of thepatch 802. The electronic field at the aperture of each slot can bedecomposed into X and Y components as illustrated in FIG. 9. The Ycomponents are out of phase and cancel out because of the halfwavelength transmission line 804. The radiating fields can be determinedby treating the antenna as an aperture 900 as shown in FIG. 9 having awidth W 902 and a height h 904.

The transmission line model can be further analyzed in the followingmanner. G_(r) is the slot conductance and B_(r) is the slot susceptance.They may be determined according to the equations:

$G_{r} = \left\{ {{\begin{matrix}\frac{W^{2}}{90\lambda_{0}^{2}} & {for} & {W < \lambda_{0}} \\\frac{W}{120\;\lambda_{0}} & {for} & {W > \lambda_{0}}\end{matrix}B_{r}} = \frac{2{\pi\Delta}\; l\sqrt{ɛ_{eff}}}{\lambda_{0}Z_{0}}} \right.$

The input admittance of the patch antenna 110 can be approximated as:

$Y_{in} = {Y_{slot} + {Y_{0}\frac{Y_{slot} + {{jY}_{0}{\tan\left( {\beta\left( {L + {2\Delta\; l}} \right)} \right)}}}{Y_{0} + {{jY}_{slot}{\tan\left( {\beta\left( {L + {2\Delta\; l}} \right)} \right)}}}}}$where Δl is the end effect of the microstrip.The rectangular patch antenna 110 will resonate when the imaginary partof the input admittance goes to zero.

The end effect may be calculated according to the equation:

${\Delta\; l} = {0.412\;{h\left( \frac{ɛ_{eff} + 0.3}{ɛ_{eff} - 0.258} \right)}\frac{\left( {W/h} \right) + 0.264}{\left( {W/h} \right) + 0.8}}$${L + {2\Delta\; l}} = {\frac{\lambda_{g}}{2} = \frac{\lambda_{0}}{2\sqrt{ɛ_{eff}}}}$$ɛ_{eff} = {\frac{ɛ_{r} + 1}{2} + {\frac{ɛ_{r} - 1}{2}\left( {1 + \frac{10\; h}{W}} \right)^{- 0.5}}}$

The resonant frequency of the patch antenna 110 is given by:

$f_{r} = \frac{C}{2\sqrt{ɛ_{eff}}\left( {L + {2\Delta\; l}} \right)}$Typically the width W of the aperture is given by:

$W = {\frac{c}{2f_{r}}\left( \frac{ɛ_{r} + 1}{2} \right)^{{- 1}/2}}$

The multilayered patch antenna array 102 may transmit both HermiteGaussian beams using the processing discussed with respect to U.S.patent application Ser. No. 14/323,082 or Laguerre Gaussian beams. Whentransmitting Laguerre Gaussian beams information may be transmitted in anumber of fashions. A spiral phase plate and beam splitter approach maybe used, a dual OAM mode antenna approach may be used or the patchedantenna described herein may be utilized. These implementations would bebeneficial in both fronthaul and backhaul applications.

In order to transmit several OAM modes of order l and amplitude a_(l)^(OAM), the antenna elements must be fed by an input signal according tothe equation:

${a_{n}^{feed}\frac{1}{\sqrt{N}}{\sum\limits_{l = 0}^{N - 1}\;{a_{l}^{OAM}e^{{- j}\; 2\pi\frac{\ln}{N}}}}},{n \in \left\{ {0,\ldots\mspace{14mu},{N - 1}} \right\}},$

Note that the number of elements in the multilayer patch antenna array102 limits the number of possible OAM modes due to sampling. Due toaliasing, modes of order greater than N/2 are actually modes of negativeorders.

${b_{l^{\prime}}^{OAM} = {\frac{1}{\sqrt{N}}{\sum\limits_{p = 0}^{N - 1}\;{b_{p}^{feed}e^{j\; 2\pi\frac{{pl}^{\prime}}{N}}}}}},{p \in \left\{ {0,\ldots\mspace{14mu},{N - 1}} \right\}},{h_{pn} = {\beta\; e^{- {jkr}_{np}}\frac{\lambda}{4\pi\; r_{np}}}},{r_{pn} = \sqrt{{D^{2} + R_{t}^{2} + R_{r}^{2} - {2R_{t}R_{r}{\cos\left( \theta_{np} \right)}}},}}$${\theta_{pn} = {2{\pi\left( \frac{n - P}{N} \right)}}},{\beta = \sqrt{g_{t}g_{r}}}$Single Mode Link Budget

H_(tot) = U^(H)HU b^(OAM) = H_(tot)a^(OAM)${\frac{P_{r}}{P_{t}}(l)} = {{\frac{b_{l}^{OAM}}{a_{l}^{OAM}}}^{2} = {{\sum\limits_{p = 0}^{N - 1}\;{\sum\limits_{n = 0}^{N - 1}\;{\frac{\beta}{N}e^{{- j}\; l\;\theta_{np}}e^{- {jkr}_{np}}\frac{\lambda}{4\pi\; r_{np}}}}}}^{2}}$Asymptotic Formulation

The object is to determine an asymptotic formulation of the Link budgetat large distances, i.e. when D→+(∞), we seek the leading term for eachvalue of 1 Link budget−1 are the same.

The link budget is asymptotically given by:

${\frac{P_{r}}{P_{t}}\left( {l} \right)} = {{\frac{\lambda\;\beta}{4\pi{{l}!}}\left( \frac{{kR}_{t}R_{r}}{2} \right)^{l}\frac{1}{D^{{l} + 1}}}}^{2}$

From the Fraunhofer distance 2 (2max(R_(t),R_(r)))²/λ=200λ, the linkbudget asymptotically tends to straight lines of slope −20 (|l|+1) dBper decade, which is consistent with an attenuation in 1/D^(2|l|+2).

Asymptotic Expressions with Gains and Free Space Losses

Gains and free space losses may be determined by:

${\frac{P_{r}}{P_{t}}\left( {l} \right)} = {\frac{{Ng}_{t}}{{l}!}\left( \frac{4{\pi\left( {\pi\; R_{t}^{2}} \right)}}{\lambda^{2}} \right)^{l}\frac{{Ng}_{r}}{{l}!}\left( \frac{4{\pi\left( {\pi\; R_{t}^{2}} \right)}}{\lambda^{2}} \right)^{l}\left( \frac{\lambda}{4\;\pi\; D} \right)^{{2{l}} + 2}}$${L_{{FS}_{eq}}(l)} = \left( \frac{4\pi\; D}{\lambda} \right)^{{2{l}} + 2}$${G_{eq}(l)} = {\frac{N\; g}{{l}!}\left( \frac{4{\pi\left( {\pi\; R^{2}} \right)}}{\lambda^{2}} \right)^{l}}$

For a fixed value of |l|, each equivalent gain increases R^(2|l|) Sothat the link budget improves by a factor of R^(4|l|). On the contrary,for a fixed value of R, when |l| increases, the link budget decreasessince asymptotically the effect of D is greater than those of R_(t) andR_(r).

Referring now to FIG. 10, there is illustrated a 3-D model of a singlerectangular patch antenna designed for 2.42 GHz and only one linearpolarization. The radiation pattern for this antenna is illustrated inFIG. 11.

FIG. 12a illustrates the radiation patterns of the circular array for anOAM mode order l=0 due to the higher grating lobes. FIGS. 12b, 12c and12d illustrate the radiation patterns for the OAM mode orders in l=0(FIG. 12b ), l=1 (FIG. 12c ), and l=2 (FIG. 12d ) in the vicinity of thearray axis.

Asymptotic OAM path loss is illustrated by:

${\frac{P_{r}}{P_{t}}\left( {l} \right)} = {\frac{{Ng}_{t}}{{l}!}\left( \frac{4{\pi\left( {\pi\; R_{t}^{2}} \right)}}{\lambda^{2}} \right)^{l}\frac{{Ng}_{r}}{{l}!}\left( \frac{4{\pi\left( {\pi\; R_{t}^{2}} \right)}}{\lambda^{2}} \right)^{l}\left( \frac{\lambda}{4\pi\; D} \right)^{{2{l}} + 2}}$When assuming e-band frequencies, a distance of 1000 m and a reasonablepatch antenna element gains, other parameters may be calculatedincluding the diameter for the transmitter and receiver array rings,number of antennas, etc.

FIG. 13 illustrates the use of a multilevel patch antenna array in aparabolic antenna 1302. The multilevel patch antenna array 102 ispositioned at the focus point of a parabolic reflector 1306 to radiateits output signal 1304 to reflect off of the parabolic reflector 1306.The patch antenna array 102 is mounted to the parabolic reflector 1302via structural support members 1308. The parabolic reflector 1306reflects the multiplexed beam that may then be detected at some type ofreceiving antenna. The approach has been shown to provide a higher gainoutput for the antenna over one only including a multilevel patchantenna array 102 without a parabolic reflector 1306.

Referring now to FIG. 14, there are illustrated a number ofimplementations using the multilevel patch antenna array 102 andparabolic reflector 1306. In the axial or FriendFeed implementation1402, the patch antenna array 102 is positioned at the focal point ofthe parabolic reflector 1306 by the supports 1308 to radiate signalsdirectly into the parabolic reflector 1306 along a central axis 1404.The reflected beam will then come straight off of the parabolicreflector 1306 and parallel to each other. If the patch antenna array ismoved by an offset O form the focal point away from the parabolicreflector 1306, the reflected beam from the parabolic reflector willfocus at a particular point. In this manner by moving the array alongthe axis of the focus point the reflected beam can be focused at desiredpoints along the axis. The off axis or offset feed approach 1406positions the patch antenna array 102 off of the central axis 1404 toradiate the beam at an angle to the central axis 1404 to reflect off ofthe parabolic reflector 1306. The patch antenna array 102 is held in itsoff axis position by support member 1308.

In the Cassegrain configuration 1408, the multilevel patch antenna array102 is positioned on the primary parabolic reflector 1306 and reflectsoutward toward a convex secondary reflector 1410 held in place bysecondary reflector support members 1412. The radiated signal reflectsoff of the convex reflector 1410 at an angle similar to the off axisreflection of implementation 1406 and reflects a second time off thesurface of the parabolic reflector 1306.

Finally, the Gregorian implementation 1414 mounts the multilevel patchantenna array 102 on the surface of the parabolic reflector 1306 toproject outward toward a concave secondary reflector 1416. The secondaryreflector 1416 is supported by secondary reflector supports 1418. Thesignal radiated by the multilevel patch antenna array 102 reflects offof the secondary reflector 1416, and a second time off of the primaryparabolic reflector 1306. Each of these cases direct the HermiteGaussian, Laguerre Gaussian, orthogonal function multiplexed beamoutward toward a receiver.

The asymptotic OAM path loss using a parabolic antenna revises theprevious loss equations in the following manner:

${\frac{P_{r}}{P_{t}}\left( {l} \right)} = {\frac{{Ng}_{t}}{{l}!}\left( \frac{4{\pi\left( {\pi\; R_{t}^{2}} \right)}}{\lambda^{2}} \right)^{l}\frac{{Ng}_{r}}{{l}!}\left( \frac{4{\pi\left( {\pi\; R_{t}^{2}} \right)}}{\lambda^{2}} \right)^{l}\left( \frac{\lambda}{4\pi\; D} \right)^{{2{l}} + 2}G_{New}}$The term G_(New) comprises the new variable arising due to the parabolicantenna. As previously discussed, assuming e-band frequencies, adistance of 1000 m and a reasonable patch antenna element gains, otherparameters may be calculated including the diameter for the transmitterand receiver array rings, number of antennas, etc.

The new loss equation may be further solved in the following manner:

${\frac{P_{r}}{P_{t}}\left( {l} \right)} = {\frac{{Ng}_{t}}{{l}!}\left( \frac{4{\pi\left( {\pi\; R_{t}^{2}} \right)}}{\lambda^{2}} \right)^{l}\frac{{Ng}_{r}}{{l}!}\left( \frac{4{\pi\left( {\pi\; R_{t}^{2}} \right)}}{\lambda^{2}} \right)^{l}\left( \frac{\lambda}{4\pi\; D} \right)^{{2{l}} + 2}G_{New}}$$\mspace{79mu}{G_{New} = {\frac{4{\pi\left( {\pi\; R_{A}^{2}} \right)}}{\lambda^{2}}e_{A}}}$${\frac{P_{r}}{P_{t}}\left( {l} \right)} = {\frac{{Ng}_{t}}{{l}!}\left( \frac{4{\pi\left( {\pi\; R_{t}^{2}} \right)}}{\lambda^{2}} \right)^{l}\frac{{Ng}_{r}}{{l}!}\left( \frac{4{\pi\left( {\pi\; R_{t}^{2}} \right)}}{\lambda^{2}} \right)^{l}\left( \frac{\lambda}{4\pi\; D} \right)^{{2{l}} + 2}\frac{4{\pi\left( {\pi\; R_{A}^{2}} \right)}}{\lambda^{2}}e_{A}}$Where R equals the radius of the parabolic antenna and e_(A) is theaperture efficiency of the parabolic antenna 0.55 to 0.70.

Referring now to FIG. 15, a hybrid patch antenna 1502 and parabolicreflector 1504 uses a single reflection to generate an OAM beam. Thepatch antenna 1502 is placed at the focal point of the parabolicreflector 1504. As discussed previously, the case of double reflectionwherein the patch antenna 1502 is placed at the feed of a Cassegrainantenna (see FIG. 14 reference number 1408 and 1414) and the generatedOAM beams are reflected twice by a sub reflector and by the parabolicreflector. FIG. 16 illustrates simulated power as a function of atransmission distance considering both the OAM beam divergence as wellas the blocking affect of a patch antenna. All the power in the exampleillustrated in FIG. 16 is normalized to the total power covered by theparabolic reflector. In the example illustrated in FIG. 16, theparabolic reflector is 4 feet in diameter.

The receiver sensitivities of commercially available millimeterwavecommunications systems have been reviewed as listed below in Table A.The potential transmission distance of using a hybrid patch antenna andparabolic dish as the transmitter taking into consideration thecommercially available receiver sensitivities is illustrated.

Estimated distance of our approach in this commercial system(transmitter power, parabolic dish diameter) Highest Receiver 10 dBm, 30dBm, 10 dBm, 30 dBm, Company Model Frequency data rate sensitivity 4feet 4 feet 8 feet 8 feet Fujitsu GX4000 70/80 3 −54 dBm 1 km for 1.8 kmfor 1.8 km for >3 km for GHz Gbps OAM 1, OAM 1, OAM 1, OAM 1, 400 m for700 m for 1.2 km for 2 km for OAM 2 OAM 2 OAM 2 OAM 2 E-band E-Link70/80 1.25 −66 dBm 1.4 km for 2.5 km for 2.5 km for >3 km for communi-1000Q GHz Gbps OAM 1, OAM 1, OAM 1, OAM 1, cations 500 m for 800 m for1.6 km for 2.5 km for OAM 2 OAM 2 OAM 2 OAM 2 E-Link 70/80 3 −48 dBm 800m for 1.5 km for 1.5 km for 3 km for Eagle GHz Gbps (estimated) OAM1,OAM 1, OAM 1, OAM 1, 350 m for 500 m for 1 km for 1.7 km for OAM2 OAM 2OAM 2 OAM 2 Bridge GE60 60 1 −60 dBm 1.2 km for 2.2 km for 2.2 km for >3km for Wave GHz Gbps (estimated) OAM 1, OAM 1, OAM 1, OAM 1, 400 m for700 m for 1.5 km for 2.2 km for OAM 2 OAM 2 OAM 2 OAM 2 AR60 60 1 −60dBm 1.2 km for 2.2 km for 2.2 km for >3 km for GHz Gbps (estimated) OAM1, OAM 1, OAM 1, OAM 1, 400 m for 700 m for 1.5 km for 2.2 km for OAM 2OAM 2 OAM 2 OAM 2 AR60X 60 1 −70 dBm 1.6 km for 3 km for >3 km for >3 kmfor GHz Gbps (estimated) OAM 1, OAM1, OAM 1, OAM 1, 600 m for 900 m for1.8 km for 3 km for OAM 2 OAM 2 OAM 2 OAM 2

FIG. 17 illustrates a configuration for an OAM multiplexed 60 GHz linkusing a hybrid patch and parabolic antenna 1702. The receivers 1704 areconfigured with spiral phase plates 1706 and focusing lens 1708. Thespiral phase plate 1706 demultiplexes the received OAM signals. FIG. 18illustrates another hybrid patch parabolic antenna configuration thatincludes a hybrid patch and parabolic antenna for both the transmitter1802 and receiver 1804 with no beam splitters. The configurations ofFIGS. 17 and 18 will use 60 GHz millimeter wave data links to multiplexOAM+1 and OAM−2 using the hybrid patch and parabolic antennas. Thesystem using the hybrid patch and parabolic antennas will providekilometer transmission distances.

The production of the patch antennas 110 are carried out through adesign and layout process as generally illustrated in FIG. 19, a cleanroom procedure for production of the antenna as generally illustrated inFIG. 20 and a final testing process as illustrated in FIG. 21. Referringnow to FIG. 19, the design and layout process is more particularlydescribed. Initially, the patch antenna is designed and simulated atstep 1902 using ANSYS HFSS with a microstrip feed structure. ANSYS HFSScomprises a high-frequency structural simulator. The software within thedevice stimulates 3-D full wave electromagnetic field. The ANSYS HFSScreates a GDSII file (graphic database system file used to controlintegrated circuit photomask plotting) from the HFSS simulation andexports the GDSII file to an AWR (Applied Wave Research Corporation)Microwave Office (MWO) layout at step 1904. In order to measure theantenna with ground signal ground probe feeding, a previously designconductor backed coplanar waveguide to microstrip transition design thathas been fabricated using Agilent Momentum is also imported at step 1906as a GDSII Agilent Momentum file into the AWR MWO Layout. The twodesigns are brought together at step 1908 and a weight and etchcompensation of 12 μm is added to the lateral dimensions to account forisotropic wet etch used in the fabrication process. The final GDSII filefor the layout is exported at step 1910 and provided to a clean room forfabrication at step 1912.

Referring now to FIG. 20, there is illustrated the clean room processfor patterning a copper layer on the FR408 laminate. Initially, thedouble-sided Cu FR408 laminate is cut using scissors at step 2002 to anappropriate size (typically 1.5″×1.5″). The FR408 laminate is cleaned byrinsing the laminate at step 2004 with acetone, isopropanol (IPA) andnitrogen (N₂) and dried in a solvent hood or using program 2 of a CPKSolvent Spinner with the appropriate chuck. The laminate is dehydratebaked at 130° C. for two minutes on a hot plate (for example, a ColeParmer digital hotplate) at step 2006. Next, at step 2008,hexamethyldisilizane (HMDS) is deposited on the laminate by a rainmethod using a Yield Engineering YES—310 vacuum hood oven. The laminatesamples are placed in the HMDS oven for 20 minutes to improve resistadhesion. Next, at step 2010, the mask is cleaned using program 2 of aCPK Solvent Spinner with the appropriate chuck. The mask is furthercleaned using an automated mask cleaner (Ultratech Mask Cleaner) usingprogram 0 DIW only at step 2012.

The lithography process is performed at steps 2014-2034. First, ShipleyS1813 photoresist is spun on to the backside of the laminate at step2014 to protect the ground layer using for example a Brewer Science CeeSpin Coater System. In one embodiment, the spin coater system willoperate at 3000 rpm with 3000 rpm/s for 60 seconds. The sample is softbaked at step 2016 at 115° C. for 90 seconds on a hot plate and hardbaked at step 2018 at 130° C. for 60 seconds on the hotplate. S1813resist is spun onto the top side pattern copper layer at step 2022. Inone embodiment, this is carried out at 3000 rpm with 3000 rpm/s for 60seconds. The sample is soft baked at 115° C. for 90 seconds on a hotplate at step 2022. The top side of the sample is exposed at step 2024with 110 mJ/cm2 using Karl Suss MA6 BA6 Contact Aligner/Printer. Next,the circuit is developed at step 2026 with Microposit MF-319 for 60seconds in a beaker. The sample is rinsed with deionized water (DIW) andN₂ in a base hood. A reactive ion etching process is performed at step2032 to remove excess photoresist using Techniques Series 85 RIE. Thisis achieved by applying O₂ only at 180 mTorr with 50 W for 15 seconds.The sample is hard baked at step 2034 at 130° C. for 60 seconds on a hotplate. The lithography is checked at step 2036 under a Leica Inm Opticalmicroscope to make sure the lithography is correct and that the gaps aredefined and not overdeveloped.

The 12 μm copper layer is etched at steps 2038-2046. The copper isetched in one minute intervals at step 2038 by agitating the sample in aCu etchant. Inquiry step 2040 determines if the Cu etching process iscomplete, and if not, the sample is rotated at step 2042 by 90° andreturns to agitate the sample within the Cu etchant at step 2038. Wheninquiry step 2040 determines that the Cu etching process is completedcontrol passes to step 2044 wherein the sample is rinsed with DIW and N₂and dried within a base hood. The sample is checked at inquiry step 2046using a microscope to determine if the Cu has been completely removed.If not, control passes back to step 2038 for further agitation withinthe Cu etchant. If all of the Cu has been removed control passes to thestripping of the photoresist process.

The stripping of the photoresist occurs by first rinsing the sample withacetone, IPA, DIW and N₂ and drying within a solvent hood or usingprogram 2 in CPK Solvent Spinner with the appropriate chuck. The sampleis dehydrate baked at step 2050 at 130° C. for five minutes on a hotplate. The etched laminate samples are examined at step 2052 under amicroscope to make sure that gaps are etched with no over etching ofareas within the sample.

The created patch antenna may be tested as illustrated in FIG. 21 toconfirm operation of the antenna. Initially, at step 2102, a DC test isperformed upon the antenna to make sure that the G-S-G feed is notshorted. An RF test is performed at step 2104 to measure the S₁₁-ReturnLoss across the frequency bands using Agilent VNA on Cascade M150 probestation. The radiation pattern of the antenna may then be measured atstep 2106 at the appropriate frequencies using a NSI spherical nearfield scanner.

It will be appreciated by those skilled in the art having the benefit ofthis disclosure that this patch antenna array for transmission ofHermite-Gaussian and Laguerre-Gaussian beams provides for thetransmission of multiplexed Hermite Gaussian and Laguerre Gaussian modesin a single transmission beam. It should be understood that the drawingsand detailed description herein are to be regarded in an illustrativerather than a restrictive manner, and are not intended to be limiting tothe particular forms and examples disclosed. On the contrary, includedare any further modifications, changes, rearrangements, substitutions,alternatives, design choices, and embodiments apparent to those ofordinary skill in the art, without departing from the spirit and scopehereof, as defined by the following claims. Thus, it is intended thatthe following claims be interpreted to embrace all such furthermodifications, changes, rearrangements, substitutions, alternatives,design choices, and embodiments.

What is claimed is:
 1. A multi-level antenna array, comprising: aplurality of patch antennas; a plurality of layers, each of theplurality of layers separated from each other by a distance, each of theplurality of layers further supporting a portion of the plurality ofpatch antennas; a plurality of connectors, each of the plurality ofconnectors associated with one of the plurality of layers, for supplyinga signal for transmission by the associated layer; a feed network oneach of the plurality of layers for providing a connection between aconnector of the plurality of connectors associated with the layer andthe portion of the plurality of patch antennas located on the layer;wherein each layer of the plurality of layers transmits the signalhaving a different orthogonal function applied thereto that multiplexeseach of the signals having the different orthogonal function appliedthereto onto a single transmission beam; and a parabolic reflector forreflecting the single transmission beam from the plurality of layers ofthe multi-level antenna array.
 2. The multi-level antenna array of claim1 further including a secondary reflector for receiving the singletransmission beam from the plurality of layers of the multi-levelantenna array and directing the single transmission beam toward theparabolic reflector.
 3. The multi-level antenna array of claim 1,wherein the plurality of layers of the multi-level antenna array areplaced at a focal point of the parabolic reflector.
 4. The multi-levelantenna array of claim 1, wherein the different orthogonal functioncomprises one of a Hermite-Gaussian function, a Laguerre-Gaussianfunction or an Ince-Gaussian function.
 5. The multi-level antenna arrayof claim 1, wherein the plurality of patch antennas in each of theplurality of layers are configured in at least one of a rectangular,circular or elliptical configuration.
 6. The multi-level antenna arrayof claim 1, wherein each of the plurality of patch antennas on a layerof the plurality of layers have a different phase applied thereto. 7.The multi-level antenna array of claim 1, wherein the singletransmission beam is transmitted on a single frequency.
 8. Themulti-level antenna array of claim 1, wherein the different orthogonalfunction comprises one of a Jacobi polynomial function, Gegenbauerpolynomial function, Legendre polynomial function, Chebyshev polynomialfunction, Legendre function, Bessel function or prolate spheroidalfunction.
 9. A system for transmitting a transmission beam comprising: atransmitter including a first multi-level patch antenna array formodulating and transmitting the transmission beam, the first multi-levelpatch antenna array further comprising: a first plurality of patchantennas; a first plurality of layers, each of the first plurality oflayers separated from each other by a distance, each of the firstplurality of layers further supporting a portion of the first pluralityof patch antennas; a first plurality of connectors, each of the firstplurality of connectors associated with one of the first plurality oflayers, for supplying a signal for transmission by the associated layer;a first feed network on each of the first plurality of layers forproviding a connection between a first connector of the first pluralityof connectors associated with the layer and the portion of the firstplurality of patch antennas located on the layer; wherein each layer ofthe first plurality of layers transmits the signal having a differentorthogonal function applied thereto that multiplexes each of the signalshaving the different orthogonal function applied thereto onto a singletransmission beam; and a first parabolic reflector for reflecting thesingle transmission beam from the first plurality of layers of themulti-level antenna array; a receiver including a second multi-levelpatch antenna array for receiving and demodulating the transmissionbeam, the second multi-level patch antenna array further comprising: asecond plurality of patch antennas; a second plurality of layers, eachof the second plurality of layers separated from each other by adistance, each of the second plurality of layers further supporting aportion of the second plurality of patch antennas; a second plurality ofconnectors, each of the second plurality of connectors associated withone of the second plurality of layers, for supplying a signal receivedby the associated layer; a second feed network on each of the secondplurality of layers for providing a connection between a connector ofthe second plurality of connectors associated with the layer and theportion of the second plurality of patch antennas located on the layer;wherein each layer of the second plurality of layers receives the signalhaving the different orthogonal function applied thereto thatdemultiplexes each of the signals having the different orthogonalfunction applied from the single transmission beam; and a parabolicreflector for reflecting the single transmission beam to the pluralityof layers of the multi-level antenna array.
 10. The system of claim 9further including a secondary reflector for receiving the singletransmission beam from the first plurality of layers of the multi-levelantenna array and directing the single transmission beam toward thefirst parabolic reflector.
 11. The system of claim 9, wherein the firstplurality of layers of the multi-level antenna array are placed at afocal point of the first parabolic reflector.
 12. The system of claim 9,wherein the different orthogonal function comprises one of aHermite-Gaussian function, a Laguerre-Gaussian function or anInce-Gaussian function.
 13. The system of claim 9, wherein the firstplurality of patch antennas in each of the first plurality of layers areconfigured in at least one of a rectangular, circular or ellipticalconfiguration.
 14. The system of claim 9, wherein each of the firstplurality of patch antennas on a layer of the first plurality of layershave a different phase applied thereto.
 15. The system of claim 9,wherein the single transmission beam is transmitted on a singlefrequency.
 16. The system of claim 9, wherein the different orthogonalfunction comprises one of a Jacobi polynomial function, Gegenbauerpolynomial function, Legendre polynomial function, Chebyshev polynomialfunction, Legendre function, Bessel function or prolate spheroidalfunctions.
 17. A multi-level antenna array, comprising: a plurality ofpatch antennas; a plurality of layers, each of the plurality of layersseparated from each other by a distance, each of the plurality of layersfurther supporting a portion of the plurality of patch antennas; aplurality of connectors, each of the plurality of connectors associatedwith one of the plurality of layers, for supplying a signal fortransmission by the associated layer; a feed network on each of theplurality of layers for providing a connection between a connector ofthe plurality of connectors associated with the layer and the portion ofthe plurality of patch antennas located on the layer; wherein each layerof the plurality of layers transmits the signal having a differentorthogonal function applied thereto that multiplexes each of the signalshaving the different orthogonal function applied thereto onto a singletransmission beam.
 18. The multi-level antenna array of claim 17,wherein the different orthogonal function comprises one of aHermite-Gaussian function, a Laguerre-Gaussian function or anInce-Gaussian function.
 19. The multi-level antenna array of claim 17,wherein the plurality of patch antennas in each of the plurality oflayers are configured in at least one of a rectangular, circular orelliptical configuration.
 20. The multi-level antenna array of claim 17,wherein each of the plurality of a patch antennas on a layer of theplurality of layers have a different phase applied thereto.
 21. Themulti-level antenna array of claim 17, wherein the single transmissionbeam is transmitted on a single frequency.
 22. The multi-level antennaarray of claim 17, wherein the different orthogonal function comprisesone of a Jacobi polynomial function, Gegenbauer polynomial function,Legendre polynomial function, Chebyshev polynomial function, Legendrefunction, Bessel function or prolate spheroidal functions.